IntroductionPreliminary remarksPreliminary remarks, cont.Preliminary remarks, concludedSome motherhood statementsThe simplest cDNA microarray data analysis problem is identifying differentially expressed genes using one slidePowerPoint PresentationSlide 9The second simplest cDNA microarray data analysis problem is identifying differentially expressed genes using replicated hybridizationsApo AI experiment (Matt Callow, LBNL)Slide 12Which genes have changed? When permutation testing possibleHistogram & normal qq-plot of t-statisticsWhat is a normal qq-plot?Why do a normal q-q plot?Slide 17Useful plots of t-statisticsWhich genes have changed? Permutation testing not possibleResults from 4 replicatesPoints to noteSlide 22Slide 23Slide 24What have we concluded?An empirical Bayes storySlide 27B=LOR compared with t and M.Extensions include dealing withSummary (for the second simplest problem)Acknowledgments1Lecture 20, Statistics 246,April 6, 2004 Identifying expression differences in Identifying expression differences in cDNA microarray experimentscDNA microarray experiments2Introduction Many microarray experiments are carried out to find genes which are differentially expressed between two (or more) samples of cells. Examples abound:•cells (from the liver, say), in a mouse with a gene knocked out, compared with liver cells in a normal mouse of the same strain•cells in one region of the brain (say cerebellum), compared with cells in a different region (say the anterior cingulate region)•tumor cells in some organ (say the liver), compared with normal cells from the same organ•cells from an organism (say yeast) after a treatment (say by heat, or cold, or a drug) compared with cells of the same kind in the untreated state•cells from some part of a developing organ or organism at one time, compare with cells of the same kind at a later time, and so on It should be clear that the number of such comparisons is limited only by the imagination of the biologist, at least at the moment, when details of so many genetic programs (drug response, development, tumorigenesis, ..) are incomplete.3Preliminary remarks Initially, comparative microarray experiments were done with few, if any replicates, and statistical criteria were not used for identifying differentially expressed genes. Instead, simple criteria were used such as fold-change, with 2-fold being a popular cut-off. This was sometimes done without regard to the variability present in the experiment, and, depending on the experiment, could be too liberal, naming genes that were not differentially expressed (false positives, or errors of the first kind), or too conservative, failing to identify genes that were differentially expressed (false negatives, errors of the second kind). The relative importance of false positives and false negatives, depends on the context: the aims of the experiment (e.g. were the investigators seeking broad patterns, or specific genes), and the follow-up experiments envisaged (e.g. validation of findings by a more precise technique). It did not take long for people to want to assign statistical significance to their findings concerning differentially expressed genes. Could p-values be attached, confidence statements be made, and so on? These questions raised a number of issues which were unfamiliar to the molecular biologists doing the experiments: replication, systematic versus random differences, multiplicity of tests, etc.4Preliminary remarks, cont. It was eventually realized on that biological replicates are important for reaching statistically sound conclusions, but even here the story is not simple, as many systematic features remain even in experiments with “independent” replicates. The fact that many thousands of comparisons were being carried out made use of traditional cut-offs (+/- 2SD, or p < 0.05) inappropriate also became clear to people. Strict control of type 1 error rates (we’ll be more precise in the next lecture) turned out to be asking too much in this microarray context, and different criteria for “controlling” errors rates have come to the fore, most notably false discovery rates (FDR). However, there still remains a need for appropriate theory. Modelling large-scale microarray experiments is not a simple task: the difference between assuming and actually having independence can be great. Where are we now? Depending on the context, some researchers can make use of traditional multiple testing procedures. Others make use of FDR notions, which are more widely applicable, but lead to weaker conclusions. Yet others have realized that is is unreasonable (given their sample sizes) to expect “statistical significance” for all their results, and instead seek evidence of “biological significance”, and validation by suitable follow-up.5Preliminary remarks, concluded Where are we now?, cont. Two issues have come to the fore in recent years. The first is the interpretation of the lists of genes determined (by whatever means) to be differentially expressed: What kinds genes are they, i.e. what is their function (DNA binding, protease,..) ? What cellular pathways or processes are involved (replication, cell death..)? Where in the cell are these genes operating (in ribosomes, mitochondria,..)? The question becomes: are genes of a given class over-represented in the list of differentially expressed genes? As there are many classes, there are many such questions, and so the issue of multiplicity comes up once more. The second is the determination of significance for sets of genes given a priori, attempting to answer some form of the question: is this (specific) set of genes differentially expressed? The idea here is that a particular set of genes (say those involved in oxidative phosphorylation) might have all or many changed a little, and that this pattern of change might be “significant”, although the individual changes are not. Of course we won’t begin with just one set of genes, but many, so multiplicity questions arise here too. In both of these questions, how we rank the genes will be important, and the cut-offs less so.6Some motherhood statements Important aspects of a statistical analysis include:•Tentatively separating systematic from random sources of variation•Removing the systematic and quantifying the random, when the system is in control•Identifying and dealing with the most relevant source of variation in subsequent analyses
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